The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  X  1  1  1  1  1  1 X^2  1 X^2  1 X^3  0  1 X^2  X  1  X X^2  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^2 X^3  0 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3  0  0  0 X^3 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^2 X^2  0 X^3+X^2 X^3  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2 X^2  0  0 X^3 X^2 X^3 X^3 X^2  0 X^3+X^2 X^2 X^2 X^3  0 X^2  0  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^2 X^3
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+54x^41+109x^42+192x^43+234x^44+272x^45+361x^46+332x^47+235x^48+104x^49+47x^50+36x^51+18x^52+16x^53+11x^54+12x^55+7x^56+2x^57+4x^59+1x^72

The gray image is a linear code over GF(2) with n=368, k=11 and d=164.
This code was found by Heurico 1.16 in 1.59 seconds.